Tone Control Filter

[The Electrician]

The following data is organized with all the resistor values first, then a table that shows the frequency response for two different frequencies 45Hz and 10kHz, which are most interesting, and that data is shown for three different settings of both pots as indicated, where each pot (one side) is set to either 0k, 10k, or 20k, as shown. The gain is then shown in db to the far right.

In the first post, the OP said:

"This circuit is designed to cut the bass, mid and treble -26db and to boost them 6db. It works fine "

Your numerical results seem to show the opposite--boost of 20+ db and cut of 8 or so db. Have I misinterpreted your results?

 

[ronv]

The circuit has a nominal gain of about 15, so -11 to +21 db.

 

[The Electrician]

The circuit has a nominal gain of about 15, so -11 to +21 db.

Yes, I see that.

When the OP said "This circuit is designed to cut the bass, mid and treble -26db and to boost them 6db. It works fine ", he was leaving out the fixed 15 db gain. It seems to me that it would be less confusing to stick with the OP's manner of speaking and only deal with the tone control stages' action.

 

[The Electrician]

Here are a couple of images showing the response of the circuit with the fixed gain set to zero.

The first image shows the response with the component values given by the OP. The bass control is not providing a shelf type response which is rather atypical; it's more like a mid response. There should be a capacitor across the bass pot, and no capacitor in series with the wiper to get a shelf response.

The 22 pF capacitor (C16) is causing a bit of HF rolloff.

The curves are close together when boosting and not so close together for a cut. A pot with a taper could help make a more even characteristic.

The second image shows the response with R17 and R22 changed to 3k3 and R25 changed to 2k7. I reduced C16 to 2 pF to display its effect on the HF response of the mid circuit.

 

[reap461]

Hi thanks for the time and effort you put in its really appreciated, I have been told to lower C13 to 820pf to avoid high frequency rolls to early when changing r22 to 3k3 do you think that's correct.

 

[MrAl]

In the first post, the OP said:

"This circuit is designed to cut the bass, mid and treble -26db and to boost them 6db. It works fine "

Your numerical results seem to show the opposite--boost of 20+ db and cut of 8 or so db. Have I misinterpreted your results?

Hi there Electrician,

As i think you found out later, when we talk about 'boost' and 'cut' it is always relative to the nominal output and never an independent quantity except when the nominal output happens to be 0db. In this circuit we have an initial gain of about 5.73 which boosts everything up by about 15db.
If you look at the output results of the numbers i posted, you'll see that when both pots are set to center (one side set to 10k in a 20k pot and the other side is necessarily 10k too then) the output is around 15db. That is the nominal output without any boost or cut so that has to be the reference gain.
So yes, if you set the input to 1 you'll see the OP's original results (to some degree anyway) but it shouldnt matter too much because with frequency response plots we always have to look for the reference gain anyway.

No problem though i could easily add another column with the 0db reference gains which wouldnt be a bad idea really as you noted. I was intending to do the second part of the circuit but havent gotten to that yet, which will also show the mid band gain and how the control affects it. You're plots were very nice however and showed this pretty well too. I wanted to do a numerical analysis rather than a simulation so that i could study the component sensitivities and perhaps come up with an optimum set of values. Dont know if that's going to happen today but i'll see if i can get to it as i think it will be interesting.

 

[The Electrician]

Hi thanks for the time and effort you put in its really appreciated, I have been told to lower C13 to 820pf to avoid high frequency rolls to early when changing r22 to 3k3 do you think that's correct.

The attached image shows in red the behavior of the treble control with R22=3k3 and C13=1000 pF.

The black curves show the effect of changing C13 to 820 pF.

I leave it to you to decide which you want.

 

[The Electrician]

...I wanted to do a numerical analysis rather than a simulation so that i could study the component sensitivities and perhaps come up with an optimum set of values. Dont know if that's going to happen today but i'll see if i can get to it as i think it will be interesting.

You are apparently using the word "simulation" to mean the use of a canned Spice program such as LT spice, PSpice or Microcap in distinction to "numerical analysis". AFAIK Spice does what it does using numerical analysis. I'm guessing that when you say "numerical analysis" you mean setting up the network equations and solving them yourself, rather than letting Spice do it. However, to me, any method that involves solving network equations mathematically is simulation, compared to soldering up the circuit and making measurements.

I produced the plots by solving the network equations directly, not with a Spice program. The final expressions are cumbersome and certainly mathematical sensitivity analysis would be possible, but there are a lot of variables and massive number crunching would be involved. The sensitivities would vary with frequency and would be best presented as graphs rather than lists of numbers. It might be just as well to do what I did in the previous post and show the characteristic curves before and after changing one component. The human visual system is good at processing data in graphical form.

Of course, just showing the sensitivity of one component doesn't find an optimum set of component values. But, what will be the criterion for "optimality"; minimum sum of squares of the various sensitivities? This would require a lot of number crunching, even for a circuit as relatively simple as this one. Please do report your results if you do decide to do this!

I took the opamp gains to be ideal, not decreasing with increasing frequency, but sensitivity to opamp parameters would be one thing to investigate. For example, a phenomenon known as "Q enhancement" can take place in active networks such as this. If I make an extreme change in the opamp gain and plot the response of the treble network, the effect can be seen. I changed the opamp gain to about 3.8, which seems to be the worst case. The green curves show the response with an ideal opamp, and the red curves show the response with fixed gain of 3.8.

 

[MrAl]

Hi again Electrician,


Yes when i say 'numerical analysis' what i really mean is 'analytical analysis' followed
up by a numerical evaluation. A 'simulation' is any form of analysis where there's
only a set of models involved instead of actual physical parts connected together, but
in today's lingo 'simulation' usually refers to when someone uses a ready made program
and obviously you understood this. The better wording might have been 'circuit analysis
by hand' or something like that. That's a little misleading too i guess though, because
what i really do is throw the netlist at my NetList_To_Laplace program which spits out
the equations and then i solve the equations for all the nodes and usually pick out the
one or two of interest. Then i actually evaluate them numerically using a program that
spits out the answers much faster than i can read them.

And then a lot of times when we refer to a 'numerical analysis' we are really talking
about the way the differential equations are solved: analytically or numerically.

And yes there is some question as to why one would do this instead of using a simulator.
If we didnt need lots of results in numerical form (part of the terminology used in calling
it numerical analysis) then it would make much more sense to use a ready made simulator.
With that we could easily step values and see what the graphs look like. No prob.

But information to be analyzed by a computer is best in pure mathematical form or just
in plain old numerical form, not in graph form. The human likes to see the graphs and
make judgments, but the computer works with numbers so it needs a set (sometimes large)
of numbers to work with. That having, we can do an optimization, not by human eye, but
but computer analysis and without doubt the most exacting way to handle it.

And there are other ways of representing the result data in a more organized way than just
a list. True, a human can look at a list and make judgments, but a computer can work
wonders with a more organized list: the matrix.

Having the right matrix(s) [this starts to sound like a well known movie] we have a set of
data that represents the way the results change for every part in the circuit. Following
those changes we have systematic ways of finding optimizations for various target criteria
as well as various fit criteria so we are not limited in any way. This allows us to
explore the results in a systematic way rather than trial and error. Without the numerical
data we would have to read the graphs into the program and work from there...which of
course is possible but i felt that having the equations in the program would be a nicer
way of doing it and interesting to some degree

As far as "a lot of number crunching" you are right, but the computer does this quickly.
And this is no different than curve fitting, and if you've ever tried to fit even a
simple curve by hand and then compared the result to a curve fitting strategy then
you know what i mean. The optimization is nothing more than a curve fit.

The data usually takes the form of the deviations from the target criteria and their
derivatives, all in neat matrix form. Various fit criteria are then evaluated and the
results tested. Different fit criteria fit different applications better than others,
some would benefit from sum of squares and others from max deviation from perfection,
etc.

All that being said (little chuckle here) you noticed too that the most interesting area
of exploration is in the gains for each sub section itself. Thus maybe i'll start off
with an exploration of those three values and see what comes of it. I think you already
chose some decent values though so in a real life scenario we probably wouldnt have to
worry too much with this circuit, but it's still interesting to look at.
Also, was thinking of including in the optimization (why not right) the ability to get
the pots all centered at their mid travel points when the gain is 0db (or about 16db
overall including the first gain stage).

Yes the simulators use Gear or Trap usually. Gear usually being preferred due to
it's accuracy.

I'll have to see how the next few days go, i have other things that i have to do first.

 

[reap461]

Hi Electrician, when you simulated the circuit was any sound still passing through with all the tone pots positioned to cut. Reason asking I got a friend of mine to design a PCB board which woks fine, apart from sound which remains when pots are cut. However I am sure when I made a prototype on breadboard the circuit had no sound coming through when all pots were cut. Any help would be much appreciated thanks

 

[audioguru]

Hi Electrician, when you simulated the circuit was any sound still passing through with all the tone pots positioned to cut. Reason asking I got a friend of mine to design a PCB board which woks fine, apart from sound which remains when pots are cut. However I am sure when I made a prototype on breadboard the circuit had no sound coming through when all pots were cut.

Tone control circuits usually have equal amounts of cut and boost. They never completely cut sounds and they also never boost sounds infinitely. The amount is usually -20dB (1/10th the voltage) for a huge amount of cut to +20dB (10 times the voltage) for a huge amount of boost.

 

[reap461]

Hi audioguru thanks for your input, I know usually tone controls never completely cut the sounds out but this circuit is not a normal baxandall type. It is basically a 3 band isolator, which isolates each separate band.

 

[The Electrician]

Hi audioguru thanks for your input, I know usually tone controls never completely cut the sounds out but this circuit is not a normal baxandall type. It is basically a 3 band isolator, which isolates each separate band.

By looking at the curves in post #24, you can see that even with the controls set for maximum cut, there is still some signal passing through.

 

[MrAl]

Hi,

Just to interject a tiny note here...

I cant think of any reason why someone would want a tone control circuit that cuts completely. If the ratio of the other frequencies is much higher than the frequencies being cut the human listener's ear will be biased by the dominate frequencies and thus the ones being cut will seem like they are not even there. There's one exception i can think of and that is with 60Hz hum (line frequency hum) where we want to cut very deep to get rid of it. But that's a constant frequency so it's a little different.

 

[audioguru]

Hi audioguru thanks for your input, I know usually tone controls never completely cut the sounds out but this circuit is not a normal baxandall type. It is basically a 3 band isolator, which isolates each separate band.

A very complicated circuit with many parts can reduce interference between frequency bands.
Each frequency band is made from a very sharp highpass filter then a very sharp lowpass filter.

Speakers sometimes have a woofer driver for low frequencies, a midrange driver for mids and a tweeter driver for highs. When each driver has its own amplifier then each amplifier is fed from a fairly complicated filter.

A simple filter has a narrow band of frequencies at its peak then gradually reduces lower and higher frequencies but they are not eliminated. Here is a simple filter:

 

[reap461]

Yes audioguru I understand that, I have already built a few 24db butterwoth and Linkwitz Riley crossovers. So I understand about roll off and crossover points etc, I am just trying to fix this circuit. Look at the urei 1620 isolator to give you a better understanding of what this circuit does, thanks for the help its much appreciated.

 

[audioguru]

I am just trying to fix this circuit.

Which circuit?

Look at the urei 1620 isolator to give you a better understanding of what this circuit does

What is an "isolator"?
The Urie 1620 is a disco stereo mixer with ordinary bass and treble tone controls.